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    Trigonometry: Polar and Rectangular Coordinates

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    Convert the equation to polar coordinates and simplify.
    1. a. xy = 1
    b. (x^2 + y62)^2 = 2xy

    Express the equation in rectangular coordinates.
    2. a. r = 3sin(t)
    b. r = 4cos3(t)
    r^2 = 4sin2(t)
    r = 4/(2 + cos(t))

    © BrainMass Inc. brainmass.com June 4, 2020, 3:24 am ad1c9bdddf
    https://brainmass.com/math/trigonometry/trigonometry-polar-rectangular-coordinates-513319

    Solution Preview

    1. First x=rcos(t), y=rsin(t).
    a. Xy=1.
    (rcos(t))(rsin(t))=1
    r^2(cos(t)sin(t)=1
    r^2sin(2t)=2.
    Therefore, the polar equation is r^2sin(2t)=2.

    b. Since x^2+y^2=r^2
    (r^2)^2=2r^2cos(t)sin(t),
    We first cancel out r^2: r^2=sin(2t).
    Therefore, the polar equation is ...

    Solution Summary

    This solution converts the first equation to polar coordinates and simplifies it, and expresses the second equation in rectangular coordinates.

    $2.19

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